Eastern prince in odd places — that's a long story (4)
I believe the answer is:
epic
'a long story' is the definition.
(eg an epic poem)
'eastern prince in odd places' is the wordplay.
'eastern' becomes 'e'.
'in odd places' indicates alternate letters (only odd-numbered letters).
The alternating letters of 'prince' are 'pic'.
'e'+'pic'='EPIC'
'that's' is the link.
(Other definitions for epic that I've seen before include "Long, heroic story" , "Of heroic proportions" , "Impressively great" , "Long poem telling of great events" , "Long poem, book, film" .)